Gravesande, Willem Jacob 's, Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1

Table of contents

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[21.] Regula 1.
[22.] Regula 2.
[23.] Regula 3.
[24.] CAPUT II. De Corpore in genere.
[25.] CAPUT III. De Extenſione, Soliditate, & Vacuo.
[26.] Experimentum 1.
[27.] Experimentum 2.
[28.] CAPUT IV. De Diviſibilitate Corporis in infinitum, & parti-cularum Subtilitate.
[29.] SCHOLIUM. De Materiæ Diviſibilitate
[30.] Infinitum finito contineri.
[31.] De Spirali logaritbmicâ, & bujus menſurâ.
[32.] De infinitorum Inæqualitate
[33.] De infinitorum claſſibus.
[34.] SCHOLIUM 2. De partium Subtilitate.
[35.] CAPUT V. De cobæſione partium, ubi de Duritie, Mollitie, Fluidi-tate, & Elaſticitate agitur.
[36.] Definitio 1.
[37.] Definitio 2.
[38.] Definitio 3.
[39.] Definitio 4.
[40.] Experimentum 1.
[41.] Experimentum 2.
[42.] Experimentum 3.
[43.] Experimentum 4.
[44.] Experimentum 5.
[45.] Experimentum 6.
[46.] Experimentum 7.
[47.] Experimentum 8.
[48.] Experimentum 9. 10. 11. 12. 13.
[49.] Definitio 5.
[50.] SCHOLIUM De efſectu attractionis vitri in aquam.
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            intellige evaneſcentes, & </s>
            <s xml:id="echoid-s401" xml:space="preserve">demonſtrationes nulli Mathematicæ demon-
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            ſtrationi firmitate cedent.</s>
            <s xml:id="echoid-s402" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s403" xml:space="preserve">Clarum etiam eſt in momento evaneſcentiæ fb & </s>
            <s xml:id="echoid-s404" xml:space="preserve">FB confundi
              <lb/>
            reveraque æquales eſſe, ergo in demonſtratione quacunque in qua
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            portionem curvæ bB infinite exiguam ponimus, quia hanc evane-
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            ſcentem intelligimus, tuto lineas ut fb, & </s>
            <s xml:id="echoid-s405" xml:space="preserve">FB pro æqualibus habemus.</s>
            <s xml:id="echoid-s406" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s407" xml:space="preserve">Demonſtrationes hæ diſtingui debent a demonſtrationibus in qui-
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            bus error, licet inſenſibilis, datur, qualis eſt demonſtratio n. </s>
            <s xml:id="echoid-s408" xml:space="preserve">1222.
              <lb/>
            </s>
            <s xml:id="echoid-s409" xml:space="preserve">ex qua deducimus ſonum, ſive majorem ſive minorem, eâdem ſemper
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            velocitate per eundem aërem moveri; </s>
            <s xml:id="echoid-s410" xml:space="preserve">quod Mathematice verum non
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            eſt, ſed differentia velocitatum, quando datur, ita exigua eſt, ut
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            nulla arte percipi poſſit, quare differentiam in Phyſicis negligimus; </s>
            <s xml:id="echoid-s411" xml:space="preserve">
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            eodem modo ac in praxi geometriæ, ubi montis altitudinem conſi-
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            deramus, hanc non pro mutata habebimus, quamvis arenula adjecta
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            ſit. </s>
            <s xml:id="echoid-s412" xml:space="preserve">In talibus autem demonſtrationibus non agitur de quantitatibus
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            infinitè exiguis, ſed de quantitatibus finitis; </s>
            <s xml:id="echoid-s413" xml:space="preserve">numero enim finito
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            non modo exprimi poteſt ratio inter arenulæ diametrum & </s>
            <s xml:id="echoid-s414" xml:space="preserve">montis
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            altitudinem, ſed & </s>
            <s xml:id="echoid-s415" xml:space="preserve">inter illam diametrum & </s>
            <s xml:id="echoid-s416" xml:space="preserve">telluris diametrum, aut
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            ſi velis diſtantiam ſtellæ fixæ cujuſcunque a Tellure.</s>
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          <p>
            <s xml:id="echoid-s418" xml:space="preserve">In hiſce demonſtrationibus in quibus pro æqualibus habemus quan-
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            titates, quæ tali inſenſibili quantitate differunt, error in demonſtra-
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            tione ſenſibilis non erit, & </s>
            <s xml:id="echoid-s419" xml:space="preserve">ideò, ubi de rebus ipſis agitur, de qui-
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            bus ſenſibus dijudicamus, demonſtrationes hæ a Mathematicis jure
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            admittuntur; </s>
            <s xml:id="echoid-s420" xml:space="preserve">ex Matheſi pura removentur, quæ tamen admittit,
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            ut demonſtravimus, demonſtrationes quæ infinitè exiguas, aut eva-
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            neſcentes, quantitates pro fundamento habent.</s>
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